The coupon yield is the interest rate as indicated on the face of the bond; for example, 5% or 6%. The yield is set by the issuing corporation and is determined by the prevailing market rates at the time of issuance.

The discount yield is used by short term bonds, such as the treasury bills. These instruments are sold at a discount to par in the amount of the discount rate. For example, a a bond with a 5% discount rate will sell for 95 and the discount yield will be equal to 5 divided by 95, or 5.26%.

Current yield measures the bonds annual interest payments as a function of the price of the bond. For example, suppose a bond was trading with a 5% coupon at a price of $900. The annual coupon payment would be $50 and the current yield would be $50 / $900, or 5.55%

Finally, the speaker discusses the YTM, or yield to maturity. Yield to maturity provides you with an internal rate of return on the bond which takes coupon interest, compounding interest, and the difference between the par value of the bond and the purchase price of the bond. He walks through a simple example of how one would calculate this number.